20.1 – Volatility Smile

We had briefly looked at inter Greek interactions in the previous chapter and how they manifest themselves on the options premium. This is an area we need to explore in more detail, as it will help us select the right strikes to trade. However before we do that we will touch upon two topics related to volatility called ‘Volatility Smile’ and ‘Volatility Cone’.

Volatility Smile is an interesting concept, something that I consider ‘good to know’ kind of concept. For this reason I will just touch upon this and not really dig deeper into it.

Theoretically speaking, all options of the same underlying, expiring on the same expiry day should display similar ‘Implied Volatilities’ (IV). However in reality this does not happen.

Have a look at this image –

This is the option chain of SBI as of 4th September 2015. SBI is trading around 225, hence the 225 strike becomes ‘At the money’ option, and the same is highlighted with a blue band. The two green bands highlight the implied volatilities of all the other strikes. Notice this – as you go away from the ATM option (for both Calls and Puts) the implied volatilities increase, in fact further you move from ATM, the higher is the IV. You can notice this pattern across all the different stocks/indices. Further you will also observe that the implied volatility of the ATM option is the lowest. If you plot a graph of all the options strikes versus their respective implied volatility you will get to see a graph similar to the one below –

The graph appears like a pleasing smile; hence the name ‘Volatility Smile’ ☺

20.2 – Volatility Cone

(All the graphs in this chapter and in this section on Volatility Cone has been authored by Prakash Lekkala)

So far we have not touched upon an option strategy called ‘Bull Call Spread’, but for the sake of this discussion I will make an assumption that you are familiar with this strategy.

For an options trader, implied volatility of the options greatly affects the profitability. Consider this – you are bullish on stock and want to initiate an option strategy such as a Bull Call Spread. If you initiate the trade when the implied volatility of options is high, then you will have to incur high upfront costs and lower profitability potential. However if you initiate the position when the option implied volatility is low, your trading position will incur lower costs and higher potential profit.

For instance as of today, Nifty is trading at 7789. Suppose the current implied volatility of option positions is 20%, then a 7800 CE and 8000 CE bull call spread would cost 72 with a potential profit of 128. However if the implied volatility is 35% instead of 20%, the same position would cost 82 with potential profit of 118. Notice with higher volatility a bull call spread not only costs higher but the profitability greatly reduces.

So the point is for option traders , it becomes extremely crucial to assess the level of volatility in order to time the trade accordingly. Another problem an option trader has to deal with is, the selection of the underlying and the strike (particularly true if your strategies are volatility based).

For example – Nifty ATM options currently have an IV of ~25%, whereas SBI ATM options have an IV of ~52%, given this should you choose to trade Nifty options because IV is low or should you go with SBI options?

This is where the Volatility cone comes handy – it addresses these sorts of questions for Option traders. Volatility Cone helps the trader to evaluate the costliness of an option i.e. identify options which are trading costly/cheap. The good news is, you can do it not only across different strikes of a security but also across different securities as well.

Let’s figure out how to use the Volatility Cone.

Below is a Nifty chart for the last 15 months. The vertical lines mark the expiry dates of the derivative contracts, and the boxes prior to the vertical lines mark the price movement of Nifty 10 days prior to expiry.

If you calculate the Nifty’s realized volatility in each of the boxes, you will get the following table –

Expiry Date

Annualized realized volatility

Jun-14

41%

Jul-14

38%

Aug-14

33%

Sep-14

28%

Oct-14

28%

Nov-14

41%

Dec-14

26%

Jan-15

22%

Feb-15

56%

Mar-15

19%

Apr-15

13%

May-15

34%

Jun-15

17%

Jul-15

41%

Aug-15

21%

From the above table we can observe that Nifty’s realized volatility has ranged from a maximum of 56% (Feb 2015) to a minimum of 13% (April 2015).

We can also calculate mean and variance of the realized volatility, as shown below –

Particulars

Details

Maximum Volatility

56%

+2 Standard Deviation (SD)

54%

+1 Standard Deviation (SD)

42%

Mean/ Average Volatility

31%

-1 Standard Deviation (SD)

19%

-2 Standard Deviation (SD)

7%

Minimum Volatility

13%

If we repeat this exercise for 10, 20, 30, 45, 60 & 90 day windows, we would get a table as follows –

Days to Expiry

10

20

30

45

60

90

Max

56%

49%

41%

40%

37%

35%

+2 SD

54%

46%

42%

41%

40%

38%

+1 SD

42%

38%

36%

36%

35%

33%

Mean/Average

30%

29%

30%

30%

30%

29%

-1 SD

19%

21%

23%

24%

24%

24%

-2 SD

7%

13%

17%

19%

19%

19%

Min

13%

16%

21%

22%

21%

20%

The graphical representation of the table above would look like a cone as shown below, hence the name ‘Volatility Cone’ –

The way to read the graph would be to first identify the ‘Number of days to Expiry’ and then look at all the data points that are plotted right above it. For example if the number of days to expiry is 30, then observe the data points (representing realized volatility) right above it to figure out the ‘Minimum, -2SD, -1 SD, Average implied volatility etc’. Also, do bear in mind; the ‘Volatility Cone’ is a graphical representation on the ‘historical realized volatility’.

Now that we have built the volatility cone, we can plot the current day’s implied volatility on it. The graph below shows the plot of Nifty’s near month (September 2015) and next month (October 2015) implied volatility on the volatility cone.

Each dot represents the implied volatility for an option contract – blue are for call options and black for put options.

For example starting from left, look at the first set of dots – there are 3 blue and black dots. Each dot represents an implied volatility of an option contract – so the first blue dot from bottom could be the implied volatility of 7800 CE, above that it could be the implied volatility of 8000 CE and above that it could be the implied volatility of 8100 PE etc.

Do note the first set of dots (starting form left) represent near month options (September 2015) and are plotted at 12 on x-axis, i.e. these options will expire 12 days from today. The next set of dots is for middle month (October 2015) plotted at 43, i.e. these options will expire 43 days from today.

Interpretation

Look at the 2nd set of dots from left. We can notice a blue dot above the +2SD line (top most line, colored in maroon) for middle month option. Suppose this dot is for option 8200 CE, expiring 29-Oct-2015, then it means that today 8200 CE is experiencing an implied volatility, which is higher (by +2SD) than the volatility experienced in this stock whenever there are “43 days to expiry” over the last 15 months [remember we have considered data for 15 months]. Therefore this option has a high IV, hence the premiums would be high and one can consider designing a trade to short the ‘volatility’ with an expectation that the volatility will cool off.

Similarly a black dot near -2 SD line on the graph, is for a Put option. It suggests that, this particular put option has very low IV, hence low premium and therefore it could be trading cheap. One can consider designing a trade so as to buy this put option.

A trader can plot volatility cone for stocks and overlap it with the option’s current IV. In a sense, the volatility cone helps us develop an insight about the state of current implied volatility with respect to the past realized volatility.

Those options which are close to + 2SD line are trading costly and options near -2 SD line are considered to be trading cheap. Trader can design trades to take advantage of ‘mispriced’ IV. In general, try to short options which are costlier and go long on options which are trading cheap.

Please note: Use the plot only for options which are liquid.

With this discussion on Volatility Smile and Volatility Cone, hopefully our understanding on Volatility has come to a solid ground.

20.3 – Gamma vs Time

Over the next two sections let us focus our attention to inter greek interactions.

Let us now focus a bit on greek interactions, and to begin with we will look into the behavior of Gamma with respect to time. Here are a few points that will help refresh your memory on Gamma –

Gamma measures the rate of change of delta

Gamma is always a positive number for both Calls and Puts

Large Gamma can translate to large gamma risk (directional risk)

When you buy options (Calls or Puts) you are long Gamma

When you short options (Calls or Puts) you are short Gamma

Avoid shorting options which have a large gamma

The last point says – avoid shorting options which have a large gamma. Fair enough, however imagine this – you are at a stage where you plan to short an option which has a small gamma value. The idea being you short the low gamma option and hold the position till expiry so that you get to keep the entire option premium. The question however is, how do we ensure the gamma is likely to remain low throughout the life of the trade?

The answer to this lies in understanding the behavior of Gamma versus time to expiry/maturity. Have a look at the graph below –

The graph above shows how the gamma of ITM, ATM, and OTM options behave as the ‘time to expiry’ starts to reduce. The Y axis represents gamma and the X axis represents time to expiry. However unlike other graphs, don’t look at the X – axis from left to right, instead look at the X axis from right to left. At extreme right, the value reads 1, which suggests that there is ample time to expiry. The value at the left end reads 0, meaning there is no time to expiry. The time lapse between 1 and 0 can be thought of as any time period – 30 days to expiry, 60 days to expiry, or 365 days to expiry. Irrespective of the time to expiry, the behavior of gamma remains the same.

The graph above drives across these points –

When there is ample time to expiry, all three options ITM, ATM, OTM have low Gamma values. ITM option’s Gamma tends to be lower compared to ATM or OTM options

The gamma values for all three strikes (ATM, OTM, ITM) remain fairly constant till they are half way through the expiry

ITM and OTM options race towards zero gamma as we approach expiry

The gamma value of ATM options shoot up drastically as we approach expiry

From these points it is quite clear that, you really do not want to be shorting “ATM” options, especially close to expiry as ATM Gamma tends to be very high.

In fact if you realize we are simultaneously talking about 3 variables here – Gamma, Time to expiry, and Option strike. Hence visualizing the change in one variable with respect to change in another makes sense. Have a look at the image below –

The graph above is called a ‘Surface Plot’, this is quite useful to observe the behavior of 3 or more variables. The X-axis contains ‘Time to Expiry’ and the ‘Y axis’ contains the gamma value. There is another axis which contains ‘Strike’.

There are a few red arrows plotted on the surface plot. These arrows are placed to indicate that each line that the arrow is pointing to, refers to different strikes. The outermost line (on either side) indicates OTM and ITM strikes, and the line at the center corresponds to ATM option. From these lines it is very clear that as we approach expiry, the gamma values of all strikes except ATM tends to move towards zero. The ATM and few strikes around ATM have non zero gamma values. In fact Gamma is highest for the line at the center – which represents ATM option.

We can look at it from the perspective of the strike price –

This is the same graph but shown from a different angle, keeping the strike in perspective. As we can see, the gamma of ATM options shoot up while the Gamma of other option strikes don’t.

In fact here is a 3D rendering of Gamma versus Strike versus Time to Expiry. The graph below is a GIF, in case it refuses to render properly, please do click on it to see it in action.

Hopefully the animated version of the surface plot gives you a sense of how gamma, strikes, and time to expiry behave in tandem.

20.4 – Delta versus implied volatility

These are interesting times for options traders, have a look at the image below –

The snapshot was taken on 11th September when Nifty was trading at 7,794. The snapshot is that of 6800 PE which is currently trading at Rs.8.3/-.

Figure this, 6800 is a good 1100 points way from the current Nifty level of 7794. The fact that 6800 PE is trading at 5.5 implies there are a bunch of traders who expect the market to move 1100 points lower within 11 trading sessions (do note there are also 2 trading holidays from now to expiry).

Given the odds of Nifty moving 1100 (14% lower from present level) in 11 trading sessions are low, why is the 6800 PE trading at 8.3? Is there something else driving the options prices higher besides pure expectations? Well, the following graph may just have the answer for you –

The graph represents the movement of Delta with respect to strike price. Here is what you need to know about the graph above –

The blue line represents the delta of a call option, when the implied volatility is 20%

The red line represents the delta of a call option, when the implied volatility is 40%

The green line represents the delta of a Put option, when the implied volatility is 20%

The purple line represents the delta of a Put option, when the implied volatility is 40%

The call option Delta varies from 0 to 1

The Put option Delta varies from 0 to -1

Assume the current stock price is 175, hence 175 becomes ATM option

With the above points in mind, let us now understand how these deltas behave –

Starting from left – observe the blue line (CE delta when IV is 20%), considering 175 is the ATM option, strikes such as 135, 145 etc are all Deep ITM. Clearly Deep ITM options have a delta of 1

When IV is low (20%), the delta gets flattened at the ends (deep OTM and ITM options). This implies that the rate at which Delta moves (further implying the rate at which the option premium moves) is low. In other words deep ITM options tends to behave exactly like a futures contract (when volatility is low) and OTM option prices will be close to zero.

You can observe similar behavior for Put option with low volatility (observe the green line)

Look at the red line (delta of CE when volatility is 40%) – we can notice that the end (ITM/OTM) is not flattened, in fact the line appears to be more reactive to underlying price movement. In other words, the rate at which the option’s premium change with respect to change in underlying is high, when volatility is high. In other words, a large range of options around ATM are sensitive to spot price changes, when volatility is high.

Similar observation can be made for the Put options when volatility is high (purple line)

Interestingly when the volatility is low (look at the blue and green line) the delta of OTM options goes to almost zero. However when the volatility is high, the delta of OTM never really goes to zero and it maintains a small non zero value.

Now, going back to the initial thought – why is the 6800 PE, which is 1100 points away trading at Rs.8.3/-?

Well that’s because 6800 PE is a deep OTM option, and as the delta graph above suggests, when the volatility is high (see image below), deep OTM options have non zero delta value.

I would suggest you draw your attention to the Delta versus IV graph and in particular look at the Call Option delta when implied volatility is high (maroon line). As we can see the delta does not really collapse to zero (like the blue line – CE delta when IV is low). This should explain why the premium is not really low. Further add to this the fact that there is sufficient time value, the OTM option tends to have a ‘respectable’ premium.

Gamma Variation with Time Graph.
On this graph, due to the introduction of Surface Line, I m not able to plot the actual line of OTM, ITM and ATM exactly,
And as I am stuck on this I am not able to read those followed graphs. Could you please help me with it.

So Sir can we assume that as of the above stated graph of “Gamma vs Time to Maturity” can we mash-up that with “Gamma Variation with time” to help myself read the graph ignoring those mentioned Red Arrows ?
Will that be a good attempt to start reading 3D graphs ?

this was really educative and very informative. but where can we find volatility cone live for nifty options? Also need some help to select proper strike. where can i find high volumes, with delta and implied volatility values in table form but live during market hours? thanx for ur help

Suresh – you need to comprehend all the Greeks to identify the best possible strikes. However towards the end of this module, I will share few pointers on this. For all other variables you can use a standard B&S options calculator, which is the focus of the next chapter (chapter 21).

Volatility cone is a very interesting concept – I cant guarantee, but we will try and develop a web based tool for this sometime soon.

Sir, I am doing option trading, till date i had not write any option, just doing buy & square off both call & put option. You are explaining the things quiet easily. But i want to know from where we can plot this graph & find the right time to enter as you know for trading the option is fast process. Thanks in advance.

Deval – unfortunately Options cant be traded based on charts. As you can see there are many dimensions for Options trading which goes beyond simple charting. For successful options trading you need to develop a deeper understanding of Greeks and associated theory…which is the focus of this entire module.

Well thanks karthik/sunil. is there a way to learn how to plot the cone on MATLAB or R….i am not aware of either of them. secondly when you calculate option greeks, the inputs that are dynamic are spot price and IV. both of them change constantly. when you keep changing them on the calculator, you can see the delta and vega go up with an increase in IV. the gamma remains constant. this was for an OTM call option of bank nifty… i need to know, if we have to constantly calculate the same as the price and IV change or just decide the underlying will move by X and calculate the premium( based on delta and gamma)? i mean summing all and taking the correct strike is proving difficult. thanks.

with this information, if underlying moves by x, we know the movement of premium thanks to delta and gamma. what else can we infer? apart from the fact that the option will lose value due to theta and the impact of volatility on the premium due to vega. do comment. thanks.

Well, it is just about that 🙂 Most of the times you end up using Delta, Gamma, and IV data…the rest of the numbers helps you quantify. For example if all else stays the same I know the premium will drop by 1.7231 points t’row (thanks to Theta).

the gamma of ATM option shoots up near expiry. the gamma is also the highest for an ATM option otherwise too. the delta of an ATM is influential when the volatility is low and even more sensitive when it’s high. in fact, when it’s high the delta of strikes around the ATM is influenced too. i guess, it means buy an ATM option closer to expiry and watch it shoot up ( i.e if your directional call is right). does all this mean trading in ATM is a safer bet? thanks.

First of all, thank you to the entire team of Zerodha for initiating Varsity. I have been through the entire module of options and waiting for the rest of it. I have a request can you please throw some light on put-call ratio and how to apply it in trading.

The option chain of SBI shows different implied volatility for different strike prices. In last chapter you taught that volatility is same as standard divination. What is the reason for different IV. Is it that IV depend on other parameters as well ?

I have seen a few charts and searched on net regarding profit and loss. All say one Standard thing ” ON THE DAY OF EXPIRY “. In the previous chapters I found the BULL CALL mentioned by you . I looked for that on internet.
My question is:
1. Will the profit and loss be equal OR be the same if I decide to square off before expiry?
2. Can we make any Excel sheet for calculating Profit loss before the date of Expiry?

Waiting for your sheet sir, Please posit it ASAP. It will help lot of us… As of now i am using options oracle but the IV value differ a bit as compared with IV shown in option chain shown in NSEindia website.

Sir, in the interpretation you mentioned that “option 8200 CE, expiring 29-Oct-2015, then it means that today 8200 CE is experiencing an implied volatility, which is higher (by +2SD) than the volatility experienced in this stock whenever there are “43 days to expiry” over the last 15 months [remember we have considered data for 15 months]. Therefore this option has a high IV, hence the premiums would be high and one can consider designing a trade to short the ‘volatility’ with an expectation that the volatility will cool off.” but on checking the historical data of 8200CE for past one month in NSE website (http://www.nseindia.com/live_market/dynaContent/live_watch/get_quote/GetQuoteFO.jsp?underlying=NIFTY&instrument=OPTIDX&expiry=29OCT2015&type=CE&strike=8200.00#) the premium price never came down. Could you please explain the reason?

Hi Karthik, Can you please explain your historical volatility calculation in little more detail for 10/20/…day periods. I have tried doing this calculation with the data from NSE website, but my calculation are not matching with the numbers given by you in volatility cone. Thanks.

I have already followed your calculation and the corresponding excel sheet used by you. What I am reporting here is,
for example, the calculation for volatility cone, for 10 days windows, annualized realized volatility seems to be incorrect, eg. you reported 26% for Dec. 2014 in the table, but the correct number is 18%. Could you please provide excel sheet that you used for your realized and annualized volatility calculation for 10 day window size. Thanks for your good work.

Hi Karthik
1) For drawing Volatility Cone how can I get the data of Annualized Realized Volatility specific to x no. of days till expiry for different months?
2) In the last Delta vs IV graph how did you come to the curve with IV of 20% and 40%? (Since IV for different Strike will be different always)

I understood how to calculate daily returns and annualized returns and SD and Mean, but thing i didnt get is how to calculate mean , SD for different windows (10 day, 20,30, etc like u caluclated and tabulated the values) ..thanks

Sorry to say, but either there is some typo in Volatility cone or my full concept is wrong, i.e. In AUG 2015 Nifty dipped from 8466 — 7809 — 7945 in last 10 days before expiry, but volatility in your figure is very less. Please upload excel sheet.

Dear Karthik,
I started reading the options theory 10 days back and read all the modules twice during this period.
Today I decided to execute a virtual trade in F&O. Options calculator is available on my online trading portal.
I was slightly bullish today morning as world markets were suggesting, I decided to buy 1 lot of NIFTY Futures JAN28 @7346/-. Since the market has been highly volatile I decided to hedge the trade at the same time by buying 2 lots of options [email protected]/- at 9:51 am.( The DLETA at that level was 0.4, combined DELTA 0.8)
In the event of NIFTY going up,from your teachings I could calculate that for every point gained in NIFTY (ie for every 1 Delta earned I would lose approx 0.6 delta ie the combined delta of 2 lots of 7300PE, after taking into account the reduction in delta as the Nifty moves up 80-90 points .
The trade worked exactly that way and by EOD NIFTY futures were at 7466. ie 90 points up and the 7300PE was trading @22/- ie 26/- down and as calculated for a 90 point profit in NIFTY I lost 0.6 DELTA X 90 on the put options ie 54(in actual 52 points) point loss combined. Net profit for the trade was 90-52= 38 points it remained that at EOD.(Profit 0.4 DELTA X 90 =36 points almost correct calculations)
I was feeling FANTASTIC and thought I can now be confident about this kind of trade and trade it regularly, UNTIL tonite when I sat to review my trade I was Shaken.
What Surprised me was when I tried to apply the similar trade on FEBRUAY contract the results were bad and it was disturbing. The strikes were exactly similar ie 7300PE but I lost , for the same 90 point upmove in NIFTY I lost a total of 80 points by EOD on the combined PUT position, compared to the 52 point loss in JAN trade. The NET profit turned out to be only 10 points (90-80).
The IV were almost similar at EOD 7300 JAN was 22.4 , FEB 20.29.
Can you please explain what went wrong , why did the results vary for FEB and what would be a better trade for FEB if executed today.
My question is too long , your answer will be appreciated and will help me improve the next trade.

Avinash – I’m a bit confused about your calculation, 2 Put options each with 0.4 Delta adds up to a total delta of 0.8. So for every 1 point up move your position losses 0.8 Deltas…so for 90 points up move you are likely to lose 72 points from the total premium i.e 98. So by EOD the premium value is likely to be ard 26…i.e 98 – 73 . How did 0.6 delta feature here?

Anyway, before you understand why this does not work well for Feb, you need to understand why this worked for Jan.

It worked because we are close to Expiry, theta is peaking (remember theta acceleration), and as we approach expiry Volatility has a lesser impact on positions ass compared to the effect on premiums at the start of the series.

Since Feb is too far and there is ample time to expiry, Volatility has a far greater impact. So besides Delta, the Vega is also playing a drag on premiums.

Also, the next chapter in Options module includes a simple arbitrage example, you may want to check that for Feb!

Dear Karthik,
Thanks for the quick reply.
The reason why I calculated the combined DELTA as 0.6 is like this.
NIFTY at 7346 ,DELTA of 7300PE is 0.4, as NIFTY moves to 7400 DELTA becomes 0.3, further up 36 points it would be less than 0.3 , so instead of calculating DELTA for every 50 points change in NIFTY I took an average of 0.3 per lot X 2 lots = 0.6. So 90 points X 0.6 = 54 points drop in PE combined premium. The profit worked out to be diff of DELTA ie 0.4 X 90 =36 points, 1-2 points here and there.
But this thing about VOLATILITY having a greater impact on long duration options I was not aware of.
I do not know whether I am correct, but the results at EOD worked out that way. Kindly advise.
FOR Yesterday what would be a better HEDGE trade for FEB series I would like an example.

Volatility does make a big difference. What you did is a classic hedge i.e buy Fut and Sell options. Suggest you try out call ratio back spread or bear call ladder? These are all hedged option strategies.

Addendum to DELTA calculation:
I would like to be very transparent about my calculation as I have gained knowledge only from your portal.
At NIFTY 7346 , 7300PE DELTA : 0.4 Gamma: 0.002, GAMMA measures the rate of change of DELTA.So for an approx 100 point move, 100 x 0.002 = 0.2 Since I did not want to calculate the change for every 50 points , I took the average of 0.2 (ie 0.1) and applied it to the range and subtracted 0.1 from 0. 4 and arrived at the new DELTA of 0.3. I know It may sound crazy but hat is the way I did it.Somehow the results co- incided with the calculation pretty accurately. Boss You have to tell me wether this is correct or a mere coincidence. Based on your reply I would be able to take more rational decisions going forward

Too tedious and very exhaustive. Good for those who want to do PHD in options. In order to trade in options, one has to have understanding option geeks(Basic), OI, Max Pain. Lastly, few good option strategies.As its time for quaterly results, strangle and straddle option strategies turns out to be profitable. If one has to trade options on Intra Day basis, select liquid stocks and strike price whose detla is between 0.5 to 1 which is ITM.

How could you find the historical volatility of individual NSE stocks for each month like nifty? i was searching it in the nse only i could find the historical data of stocks but not the volatility at different time periods. we could calculate it like you showed in previous chapters.

In the above graph (delta vs implied volatility) why is that ITM of put option has delta > -1 when volatility is 40% (blue line) ?? When the volatility is more, premium increases for put option acc to http://zerodha.com/z-connect/wp-content/uploads/2014/08/put-vs-vega_v1.jpg . Then why is it that here, the delta is > -1. According to above graph (put vs vega) the delta with volatility should be better than without volatility. Correct me if I am wrong. Eagerly waiting for your response.

The put delta is capped to -1, and cannot be greater than -1…and -1 is the maximum delta a put option can gain….which is what happens when the put option is deep ITM. When Volatility increases the rate at which delta changes increases…which is what the graph is trying to convey.

Hi Karthik, kindly answer the following questions.
1) If the volatility increases, (i) delta increases (or) (ii) rate of change of delta ?
2) Isnt the rate of change of delta = gamma ?? Then, if the volatility increases gamma increases ?
3) The above graph (delta vs implied volatility) shows that, for a deep ITM call/put options with the increase in volatility, the delta plotted is 0.9/-0.9 (approx) i.e not 1/-1. How can delta at high volatilty (40%) be less than delta at low volatilty (20%) ??
4) vega talks about change in premium w.r.t change in volatility. Does vega (volatilty) effects delta as well a part from premium. Please clarify, vega vs delta;

1) Rate of change of Delta
2) Yes,but do note that the gamma peaks at ATM…which also explains why Delta is upper and lower bound
3) Think about it non mathematical terms – when Volatility increases the chance of stock moving haywire is greater…hence deep ITM options also get reactive…this is exactly why delta is not strictly 1 when volatility increases
4) Yes

Hi Karthik,
Consider the article below http://www.theoptionsguide.com/delta.aspx. They said
“As volatility rises, the time value of the option goes up and this causes the delta of out-of-the-money options to increase and the delta of in-the-money options to decrease.”
From the graph in the article, the delta of ITM comes down (from 1 to 0.95) with increase in volatility.
Doesnt delta and volatility linearly related ? From the graph, ITM options delta is not linearly related to volatility. pls clarify

Hi Karthik,
Could you explain about the below points those are getting confused and taken from Volatility Cone excel file?
1. xi-x1
2. (xi-x1)^2
3. =SQRT(1/B$5*SUM(OFFSET(Sheet1!$E$2,MATCH(Sheet1!$N5,Sheet1!$A$2:$A$504,1)-1,0,-B$5)))*SQRT(252)

I got the explanation from an excel expert(excel forum), about excel formulas used for Vitality cone calculation , please find the information below.

For example, is it the use of MATCH and OFFSET? Is it the multplication of SQRT(252)?

The formula calculates the annualized standard deviation of daily (natural) log returns, which are the values in column Sheet1!E. It is a measure of volatility.

The MATCH expression returns the row index (relative to row 2) of the closest date in column Sheet1!A before or equal to the date in Sheet1!N3.

The notation $N3 means that we use N3, N4, N5 etc as we move down each column of formulas.

In contrast, the notation $A$2:$A$504 means that we always use A2:A504 in each formula.

The OFFSET expression returns the cell range of values (log returns) from column Sheet1!E corresponding to the last B5 (number of) dates ending with the relative row index returned by MATCH.

The notation B$5 means that we use B5, C5, D5 etc as we move across each row of formulas.

In contrast, the notation $E$2 means that we always use E2 in each formula.

The expression SUM(…)/B$5 calculates the (population or exact) variance of the daily log returns referenced by OFFSET.

The expression SQRT(SUM(…)/B$5) calculates the standard deviation of the daily log returns.

The daily standard deviation is annualized by multiplying by SQRT(252) according to the “square root of time” rule, assuming 252 trade days per year (on average).

—–

The (population or exact) variance of a set of data is Sigma((x[i]-xhat)^2) / n, where x[i] is each of n data points, and xhat is the mean of the data. (The operation ^2 is the square of the calculation. Sigma is the sum of the calculations.)

Ostensibly, the values (x[i]-xhat)^2 are calculated in column Sheet1!E, based on the calculation of x[i]-xhat in column Sheet1!D.

However, the calculation in column Sheet1!D seems to be incorrect.

At a minimum, the reference to J4 in Sheet1!D3 should probably be written $J$4, so that J4 is referenced in each formula down the column.

Any update on why the volatility cone excel provided is having a reference to “J4” in sheet1 formulae.

Also i understand, it is important to understand if volatility might increase or decrease to decide on weather to go long or short on option. And we may use Volatility cone to determine if the volatility might increase or decrease. Request to confirm my understanding.

In addition, is there any other way apart from volatility cone to determine if volatility might increase or decrease.

Googled about realized volatility and found http://www.realvol.com/VolFormula.htm which explains why mean ( “J4” ) is zero as follows. Request to review and confirm.
————————–Extract from website ———————————————-
Mean Set to Zero
The RealVol Daily Formula starts with the traditional formula for standard deviation and modifies it in a few key ways. First, we set the mean to zero in order to provide “movement regardless of direction” instead of “movement about a mean or trend.” Doing so makes hedging easier for options traders and corresponds to the formula used for variance swaps and volatility swaps in the over-the-counter market.
————————–Extract from website ends ———————————————-

Thanks a lot for teaching these concepts.
My query is:
1) From delta v/s IV, can we infer that in case of high IV, gamma of OTM & ITM would not approach 0.
2) In excel sheet, in bin width why did you divide the range by 50 ?

can you please give details of calculation of volatility cone that is described in above figure ,like how do you calculate for 10 days,20,days 120 ays .All details are for calculation of standard deviation or volatility but no calculation is shown for volatility cone so kindly provide details and formula .or is there any website where we can see different-2 days historical volatility so can draw the cone and applied IV ?

While thanks for the excel sheet for volatiatlity cone but am not able to match the calculations as in sheet. I tried for 10 days for the month of dec but am not able to match the stdev atleast although followed the process as described in earleir chapters. It would be nice if the person who has done calculations takes the pain to explain atleast for a month. This would be a great learning to all of us.
Thanks for good work

Hello, i have tried tinkering with the volatility cone model in excel but seems there is an error. I see that you have cracked it , so can you please post the same for my and others benefit? Also, i would be requiring the same for Bank nifty , so it would require fresh data inputs

helllo karthik sir its really a superb information you have providing with easy to understand language. I am also doing my research on options and facing certain difficulties regarding it, how can we plot date vs implied volatility chart (irrespective of strike) ?? How this after some study i found that india vix does this for nifty but i am looking same for individual FnO stocks. Tried backsolving from black scholes but it gives IV for particular strike. India vix formula is bit complex plus it needs bid and ask rates to backtest it, historical bid ask rates are not available please let me know regarding this thanx a ton!!

This is not an easy task for the exact reason you’ve mentioned. ViX computation is highly complex and data intensive. Without the historical order book and knowledge on cubic spline it is difficult to do this.

True, this is exactly what the ‘Volatility Smile’ suggests. Volatility should be the same across all strikes, but this is only in theory. The variation in IV’s can mathematically attributed to something called ‘Jump diffusion’.

Thanks Kartik for your reply.
In the Volatility Cone excel, frank I could not decipher anything from the sheet.
But I went for a much much longer process.
With the expiration dates for the last 15 months(Is it necessary to take 15 months .??), I calculated the Annualized Volatility 10,20,30,45,60,90 days from the expiry separately for each 15 months.
Very long and tedious, but kind of the concept is same. ( Correct.. ??)
After that with that data one can construct the Cone.
But please it would be of much help if one can give the details of the Calculations in the Zerodha VC excel.
One user gave it, but still it is not making any sense to me.

Hi Karthik,
Thanks a ton for your constant support.
Well, I have deciphered the values for the current Nifty series.
The values look quite good to me, but I am not an expert in charts and can not plot this table hence.
I request you to plot the below values for yourself and see if the Cone is coming.
If it is a success kindly do let me know the process also.
Thanks again.

Hi Dear Karthik,
Do we have to draw Volatility cone for each and every strike price.
I suppose, one cone will not give clarity on IV, for all the strike prices of the same underlying.
Could you please help me on this.
Regards

Hi Karthik,
I am thankful that you created such a content as it helps new users like me and others, please continue the good work. I looked for a tool and found Options Oracle tool is capable of creating a volatility cone. I am yet to check the accuracy of it but others here could also check and feedback if they feel it is plotting the call and puts IV properly.http://www.pasitechnologies.com/2015/11/optionsoracle-nse-plugin-v-185.html

A scrip is considered liquid if you can easily buy or sell the contract when you place a market order. Do note, the price at which you get the contract should be around the same price as the last traded price in the market.

Based on your Volatility Excel, I have put in 15 months data for Nifty to get the volatility cone for the last 12 months. From the volatility cone, a 30 days-to-expiry option with + 2 SD variance would be at an IV of 18.37%. Now from the Nifty Option chain, as on today (28th Mar), the 27-Apr 10000 PE has an IV of 20.47%. The option also has a good liquidity at the moment, going by the Volume and OI figures. Is it feasible to go short on this 10000 PE which is presently trading at 835 ?

Thanks for the feedback. Another Question.. For plotting the volatility cone, the days to expiry (x axis) used was 10-20-30-45-60-90. Is this fixed or can it be changed/expanded to, say 10-15-20-25-30-35-45-60-75-90?

Hi karthik,
I have two queries
Kindly guide.
1) most of the time i have seen that the direction of nifty is highly dependent on the global markets and some major indian news. In that case how relevant is the nifty chart by itself ?
2) can you provide the opening time of major global markets( which affects indian markets ) w.r.t. IST ?
Thanks in advance.

i am trying my level best to understand this formula =SQRT(1/B$5*SUM(OFFSET(Sheet1!$E$2,MATCH(Sheet1!$N5,Sheet1!$A$2:$A$504,1)-1,0,-B$5)))*SQRT(252), so as to obtain the value for x days for given month. but cant able to achieve so far. i tried the formula you explained in chapter 16. but not getting this value as shown in excel sheet. If you can shown how to obtain relative volatility , it will really helpful. please explain here or mail me. i will really appreciate

This is really good info. Is there any broker in India who gives this IV rank info inside the trading platform? Also if i just have to calculate the IV rank using the formula “100*(Current IV – 52 week Low IV)/(52 week High IV – 52 week low IV), how do i do that. I guess it will be very difficult to calculate the daily voltaility for last 364 days and then figure the high and low values..

Amazing tutorial. At a time when people hold back information and tricks of the trade for selfish reasons, there is an interesting and knowledgeable teacher like Karthik who loves to share. Learnt a lot. Thanks. Off I go to the next module!

I did not get the monthwise historic data anywhere on NSE website, secondly u said “If we repeat this exercise for 10, 20, 30, 45, 60 & 90 day windows, we would get a table as follows” where to get such precise data?

I have following questions.
1. If I want to use volatility cone to find trading opportunities, do I have to calculate this cone for each underlying in which I’m interested or these values are readily available? I know IndiaVIX is volatility index of all the stocks but I feel it won’t depict correct conditions of any particular stock.
2. I know you told there is no particular checklist while trading options, but I was hoping if you can give some steps to do before starting a trade. I read all the chapters and have understood all the concepts but when it comes to trade I still feel I might miss something since there are many factors to look at.
So not a strong checklist like you mentioned in TA but just a few steps for newbies.
Something like this I have in mind for naked trades-
Step1 – find your view on underlying ofc
Step2 – choose a expiry based on liquidity and trading time
Step3 – pick put/call strikes based on time to expiry and check premiums
Step4 – check volatility, buy when volatility is low, short when volatility is high

1) You will have to develop the Cone for each underlying. True that on ViX
2) There is a high possibility that each time you trade options, the circumstance is different. Hence difficult to generalize a checklist. Go ahead and take a trade, a low risk one…your learning curve will accelerate once you have a trade live in the market.

Once again thanks for sharing all these. I have done the Volatility Cone calculations myself, and as many others mentioned in earlier comments, I think there is some problem in the Volatility Cone excel sheet shared by you (as well as in the example used). I have done all the calculation in a Google spreadsheet with real-time data grabbed from Google finance (https://goo.gl/wUsgBd). Anybody can use this to get Volatility Cone for current date without requiring to do any change (also for any previous date by changing start date).

Anyway, as per my calculation, the mean line in Volatility Cone for the period used by you guys (Jan 11 – Feb 12) lies around 22-24. This matches with India VIX data for that period. However, in the shared excel sheet, this lies around 30 which is around the maximum India VIX level in that period. You do not need to go through either of these calculations to verify what I’m saying, but do you think the way I’m thinking is correct, i.e. mean volatility in Volatility Cone should be around the same level as India VIX average for the same period?

Moving on to my second question, in my calculation as well as in your examples, the MIN line in volatility cone is always greater than -2SD line (this is not the case with MAX and +2SD). Does this indicate anything? I was thinking may be this is a proof of what you mentioned in several chapters – “fear spreads faster than greed”. So, Nifty volatility always shoots up more from the average, than it goes down.

Vix average need not be same as avg volatility of volatility cone, but it should be close enough.
Calculation for vix is different from volatility cone. Volatility cone uses spot data, ViX uses IV of near month and next month options, so they need not match.

The mathematical reason for why highest value vix is higher than 2 sd, but lowest value is not below -2 sd is that the Volatility cone assumes a normal distribution for nifty, which is only an approximation. Think of it, volatility can never be zero or negative, whereas it has no upper limit. This is not the case with the normal distribution, it will swing on both sides with equal chance. That’s the reason for this pattern.

Thanks Karthik for the reply below (can’t reply to that for some reason).

Also wanted to mention that last week was the first time I tried Option trading after going through all these material. It has been a exciting practical hands-on with Gujarat election going on. I could relate as well as predict and check all the volatility caveats you have mentioned in these articles. For example, Thursday (the day before exit poll was out), premiums of almost all 3-4 strikes on either side of ATM for both PE and CE increased although Nifty was down by some 0.4~0.5%. The reason being Volatility increased to almost 17% (highest in last 11 months). And although Nifty went up, premiums of some deep OTM CE dropped next day with exit poll bringing down the volatility to normal levels.

Hello sir,
as you explained volatility cone to measure costliness of an option by using chart above having colorfull lines of sd1,sd2 etc. it was very easy to understand that which option is costly and which is cheap for buyers perspective.BUT if am doing same exercise at my pc at home i am facing problems:-
1. How to make same chart
2. how to plot dots on that chart
yeah i can understand i can use excel for that exercise. but i wanna use same type of graphical interpretation of things that makes things easy to understand
Thank you sir.
Warm regards
Ankit